Longitudinal spin fluctuations in nickel

The longitudinal, transverse, and paramagnetic spin fluctuations in Ni have been measured near ${\mathit{T}}_{\mathit{C}}$ by means of polarized neutron scattering in the momentum range 0.06<q<0.18 A${\mathrm{̊}}^{\mathrm{-}1}$. In transverse scans, spin-wave peaks at ${\mathrm{\omega }}_{\mathit{q}}$=${\mathit{Dq}}^2$ appear as expected from previous measurements performed with unpolarized neutrons. The longitudinal fluctuations are quasielastic, in agreement with predictions of a recent mode-mode coupling theory and renormalization-group theory. The data indicate that the longitudinal dynamical scaling function is smaller than 1 just below ${\mathit{T}}_{\mathit{C}}$. The scaling function for the paramagnetic scattering is shown to be in agreement with the Résibois-Piette scaling function for energy scales up to ${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{C}}$. The measured field dependence of the scattering is rather weak, indicating that the internal fields H are rather large. Therefore it was impossible to observe the ${\mathit{H}}^{\mathrm{-}1/2}$ divergence of ${\mathrm{\chi }}_{\mathit{L}}$(q→0) that is predicted for the isotropic Heisenberg model in three dimensions. In contrast, we found ${\mathrm{\chi }}_{\mathit{L}}$(q→0)∝(1-T/${\mathit{T}}_{\mathit{C}}$ ${)}^{\mathrm{-}\gamma }$, which also appears to be a result of the internal fields. The q dependence of ${\mathrm{\chi }}_{\mathit{L}}$ is Lorentzian-like. The T dependence of the correlation length indicates critical behavior. These features closely resemble the behavior of the paramagnetic fluctuations, and they are in agreement with results obtained with use of ε-expansion techniques.